A TLC5940 can not supply any positive voltage out of it. It only acts as a current sink, that is all it does is to connect its outputs to ground.

In order for this to be converted into a signal capable of turning on a FET you have to connect a resistor, say 10K but it does not matter much what it is, from each of the TLC5940's outputs to +5V.

When you touched this with your hand, the interference you pick up was being injected into the gate of the FET. The TLC5940 then grounded this signal, turning the FET off or let the interference you pick up turn the FET on.